In a machine tool, errors may be generated in the motions of the feed axes due to the delay generated in the driving system by various causes. An example of the causes generating the motion errors includes, as well as changes in the machining load, a reverse mark which is generated when the tool path intersects a border between quadrants or when the rotation of a motor of a feed axis is reversed. In particular, a reverse mark, which is generated when a tool path intersects a border between the adjacent quadrants, is generally referred to a “quadrant protrusion”. Reverse marks are undesirable machining marks in the form of notches or protrusions generated on a machined surface when the feeding direction is revered in a cutting process for machining a circle, an arc or a curved line such as an oval or a spiral. For example, reverse marks are generated by motion errors due to the backrushes, the resilient deformations and the frictional resistances in the X-, Y- and Z-axis feed devices (ball screws, bearings and guiding devices) when the feeding directions in the respective feed axes are reversed during a process for machining a curved surface by controlling the X-, Y- and Z-linear feed axes.
The invention in Patent Literature 1 adds a predetermined accelerating speed to a speed command, when a feed axis is reversed, in order to prevent or reduce the generation of the reverse marks. Further, the invention in Patent Literature 2 prevents the generation of reverse marks, in a machine tool for cutting a workpiece by moving a rotating tool relative to a workpiece, by controlling the rotational phase of the rotating tool. Furthermore, the invention in Patent Literature 3 reduces the influence, caused by the motion errors of a machining center, on the finishing accuracy of a machined surface by generating NC data so that the direction and the magnitude of the feeding speed vector at a cutting point between the end mill and the workpiece is maintained constant.